Size-frequency distribution of crater populations in equilibrium on the Moon

Overprinting of craters by subsequent impacts and topographic degradation complicates crater statistics, especially for old surfaces and small-diameter crater populations. A crater population is regarded as in equilibrium at a particular crater size when smaller craters are being produced at the same rate at which they are being destroyed. Evaluating the equilibrium state of crater populations is challenging, and empirical equilibrium densities are frequently inferred. By performing careful crater counts and cross comparisons on several lunar surfaces, we study the size-frequency distributions (SFD) for the crater populations, which have portions in equilibrium. The results are one of the few observational constraints on the SFD of crater populations in equilibrium, showing that referring to empirical equilibrium densities is not safe for evaluating the equilibrium states of crater populations. Equilibrium densities are not positively correlated with the ages of crater populations, and some populations in equilibrium have crater densities less than those previously believed to represent equilibrium conditions. Besides the SFD of the production population, different crater removal rates at different diameters also affect the SFD of crater populations in equilibrium. The equilibrium onset diameter (D-eq) of a crater population can be translated to model ages because older populations have larger D-eq, and those for same-aged surfaces are comparable. We show that the crater populations studied here are in equilibrium at much smaller diameters than those predicted for same-aged surfaces by crater degradation models, thus indicating lower crater degradation rates on the Moon, and/or younger ages of the counting areas.